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3 years ago

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The velocity of a particle traveling along a straight line is v = Vo − ks where k is constant. If s=0 when t=0, determine the po

sition and acceleration of the particle as a function of time.

1 answer:

musickatia [10]3 years ago

4 0

Answer:

acceleration of the particle as a function of time is given as

$a(t)=-\frac{ks}{t}$

and position of the particle as a function of time is given as

$x(t)=ut+\frac{at^2}{2} \\x(t)=V_{0}t-\frac{\frac{ks(t)}{t}t^2}{2}$

$x(t)=V_{0}t-\frac{kst}{2}$

Explanation:

we have given,

$v=v_{o}− ks$

at t=0, s=0

therefore initial velocity,u

u=v= $V_{o}$

v=u+at.........(1)

we know from first equation of motion

let acceleration at time t be a(t), and position be x(t)

put value of v,u and a in equation 1

we got,

$V_{o}-ks=V_{o}+a(t)t$

Therefore,acceleration of the particle as a function of time is given as

$a(t)=-\frac{ks}{t}$

and position of the particle as a function of time is given as

$x(t)=ut+\frac{at^2}{2} \\x(t)=V_{0}t-\frac{\frac{ks}{t}t^2}{2}$

$x(t)=V_{0}t-\frac{kst}{2}$

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Answer:

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Explanation:

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mg₀ = G Mm / R²

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Given mg₀ = 400 N

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Answer:

a) Final velocity of the dragster at the end of 1.8 s = 75.6 m/s

b) Final velocity of the dragster at the end of 3.6 s = 151.2 m/s

c) The displacement of the dragster at the end of 1.8 s = 68.04 m

d) The displacement of the dragster at the end of 3.6 s = 272.16 m

Explanation:

a) We have equation of motion v = u + at

Initial velocity, u = 0 m/s

Acceleration , a = 42 m/s²

Time = 1.8 s

Substituting

v = u + at

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Final velocity of the dragster at the end of 1.8 s = 75.6 m/s

b) We have equation of motion v = u + at

Initial velocity, u = 0 m/s

Acceleration , a = 42 m/s²

Time = 3.6 s

Substituting

v = u + at

v = 0 + 42 x 3.6 = 75.6 m/s

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Initial velocity, u = 0 m/s

Acceleration , a = 42 m/s²

Time = 1.8 s

Substituting

s= ut + 0.5 at²

s = 0 x 1.8 + 0.5 x 42 x 1.8²

s = 68.04 m

The displacement of the dragster at the end of 1.8 s = 68.04 m

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Initial velocity, u = 0 m/s

Acceleration , a = 42 m/s²

Time = 3.6 s

Substituting

s= ut + 0.5 at²

s = 0 x 3.6 + 0.5 x 42 x 3.6²

s = 272.16 m

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